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C₂×#54143 #8102884

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12,14,17)(13,16,18,15)(19,20,23,25)(21,22,26,24);(3,4,6,8)(5,7,10,9)(11,13,14,18)(12,15,17,16)(19,21,23,26)(20,24,25,22);(13,18)(15,16)(20,25)(22,24);(3,4)(5,7)(6,8)(9,10)(11,13)(12,16)(14,18)(15,17)(19,22,23,24)(20,21,25,26);(3,5)(4,7)(6,10)(8,9)(11,12)(13,16)(14,17)(15,18)(19,21)(20,24)(22,25)(23,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8010080);